Question: Rewrite as a simplified fraction. ${0.23\overline{1} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 231.1111...\\ 100x &= 23.1111...\end{align*}}$ Subtracting the two equations, we have: ${900x = 208}$ ${x = \dfrac{208}{900}} $ ${x = \dfrac{52}{225}} $